Unless you're a freaky mutant with two separate mouths... no, they don't stack. Take the better one and use the other racial feature/feat for something else.

OK, thank you for the prompt reply. But what if I, well my character is anyway, a freak of nature? Say I take the Vestigial Limb discovery twice as an Alchemist and get an extra claw attack from some other source, for example a Natural Attack Ranger who takes Aspect of the Beast as their style feat.

Clarification Question.
A Witch counts as a hag for joining a Coven.
Fair enough.
Coven must contain at least one hag.
Fai . . .wait. Logically, that means that a Coven can be all witches and no Bestiary hags as they all count as hags for the purposes of joining of a Coven, which must contain at least one hag, which they count as. . .
Was this the intended interpretation?
Edit: ^:The Powah of Chevy compels thee, the Powah of Chevy compels thee! ;-)

Sneak attack applies to any attack you make with an attack roll against a foe denied their dexterity.

AKA: There's no difference between doing 3 scorching rays and three thrown daggers as far as sneak attack cares. In the vast majority of situations, the target will become aware of you after that first hit, though, so the 2nd and 3rd scorching ray or dagger would often not get sneak attack at that point.

And of course, if you're arguing that all three rays hit at once—that's effectively one attack, and that means that you only get sneak attack once. That's not how the spell's described, though.

You, sir, have set a precedent, a precedent I can link to.

For this, I thank you.
As for getting all to qualify, well, that's what Greater Invisibility is for.

Lets imagine a scenario.
Lets imagine you have a character with sneak attack and spells.
Lets imagine the spell is scorching ray.
Lets imagine this character has a high enough caster level to get more than one ray.
My question is: Can you get sneak attack, assuming you meet all other criteria, within 30 feet and denied dexterity bonus, with each ray of scorching ray?

Reading the PDF, well, its a neat idea, but I don't see how a rifle using Gunslinger can possibly keep up damage wise. Technically speaking, they can't use vital strike, and they can't use iterative attacks. Like crossbows, many of the ranged feats don't apply. Oh, and 10 gp a shot? Ouch. That especially hurts for the pistol packer, who are otherwise better off, but still can't use some of the best ranged feats. The actually having iteritives helps, especially with them being ranged touch attacks. But your going to be going through mounds of gold if you are going to be shooting off like an archer.
I like the grit mechanic, mostly, though the cauterizing barrel trick seemed awful silly to me.
Also, skill points. A few more would help.
If I seem all down, it is because I WANT to like this, I WANT guns in my fantasy.